Reading multi-layer continuous magnetic recording media

ABSTRACT

A method and system for reading readback pulse shapes representing a magnetization state transition between such written magnetization states of a two-layer continuous magnetic recording medium. A readback pulse shape representing a written magnetization state transition is read. The written magnetization state transition is uniquely identified from the readback pulse shape of the transition or from both the readback pulse shape of the transition and the readback pulse shape of one or more next magnetization state transitions.

This application is a divisional application claiming priority to Ser.No. 12/236,589, filed Sep. 24, 2008 now U.S. Pat . No. 8,107,194 B2.

FIELD OF THE INVENTION

The present invention relates to writing and reading multi-layercontinuous magnetic recording media.

BACKGROUND OF THE INVENTION

Continuous magnetic recording media are currently used for recordingbits of data thereon. With conventional continuous magnetic recording,however, there are limitations on the achievable recording density andon the efficiency of writing bits of data on the continuous magneticrecording media.

SUMMARY OF THE INVENTION

The present invention provides a method for writing magnetization statesin a multi-layer continuous magnetic medium comprising a plurality ofmagnetic layers, each magnetic layer comprising magnetic materialcontinuously distributed in an X-Y plane defined by an X direction and aY direction orthogonal to each other, consecutive magnetic layersseparated by non-magnetic spacer material and distributed along a Zdirection orthogonal to the X-Y plane, said method comprising:

selecting a magnetization state [S1; S2] comprising a magnetic state(S1) and a magnetic state (S2) in a first magnetic layer and in a secondmagnetic layer, respectively, of the plurality of magnetic layers,wherein α₁* and α₂* are a first tilt angle and a second tilt angle atwhich a hard axis of the first magnetic layer and the second magneticlayer are respectively oriented with respect to the X direction, andwherein either or both of α₁ * and α₂ * are in a range of 0 to −90degrees;

determining a write current (I) sufficient to write the magnetizationstate [S1; S2]; applying the write current I to a magnetic write headmoving in the X direction to generate in the first magnetic layer andthe magnetic second layer a magnetic field that exceeds a switchingfield of the first magnetic layer and a switching field of the secondmagnetic layer;

responsive to said applying, said magnetic write head writing themagnetization state [S1; S2] by simultaneously writing the magneticstate S1 in the first magnetic layer and the magnetic state S2 in thesecond magnetic layer.

The present invention provides a method for reading magnetic statetransitions in a two-layer continuous magnetic medium comprising twomagnetic layers, each magnetic layer comprising magnetic materialcontinuously distributed in an X-Y plane defined by an X direction and aY direction orthogonal to each other, said two magnetic layers separatedby non-magnetic spacer material and distributed along a Z directionorthogonal to the X-Y plane, said method comprising:

reading at a specific location (x) of the medium along the X direction,by a magnetic read head moving in the X direction, a readback pulseshape W(x) associated with a magnetization state transition T_(ij)(x)from a magnetization state [S1; S2], to a magnetization state [S1;S2]_(j), wherein i and j are each 1, 2, 3, or 4 subject to i≠j, whereinS1 and S2 is a magnetic state in a first magnetic layer and in a secondmagnetic layer, respectively, of the two magnetic layers, wherein thefirst magnetic layer and the second magnetic layer have a magnetic easyaxis respectively oriented at a first tilt angle (α₁) and a second tiltangle (α₂) with respect to the X direction, wherein the magnetizationstate [S1; S2]₁, [S1; S2]₂, [S1; S2]₃, and [S1; S2]₄ respectivelycorresponds to a state A=[+1,+1], a state B=[−1,−1], a state C=[+1,−1],and a state D=[−1,+1], wherein the magnetic state S1 is respectively +1or −1 if a magnetization of the first layer is oriented at or oppositethe angle α₁, wherein the magnetic state S2 is respectively +1 or −1 ifa magnetization of the second layer is oriented at or opposite the angleα₂, and wherein the first magnetic layer and the second magnetic layerhave a magnetic hard axis respectively oriented at a first tilt angle(α₁*) and a second tilt angle (α₂*) with respect to the X direction;

after said reading W(x), identifying from W(x), a set (T) ofmagnetization state transitions, wherein either 1) the set (T) consistsof T_(ij)(x) if W(x) has a pulse shape that is distinctive anddistinguishable from the readback pulse shape of each othermagnetization state transition of all possible magnetization statetransitions so as to uniquely identify T_(ij)(x) or 2) the set (T)comprises T_(ij)(x) and at least one other magnetization statetransition of the all possible magnetization state transitions whoseassociated readback pulse shape is not distinctive and distinguishablefrom the readback pulse shape of W(x);

if the set T comprises T_(ij)(x) and the at least one othermagnetization state transition, then reading, by the magnetic read headmoving in the X direction, a next M readback pulse shapes denoted asW(x₁), W(x₂), . . . W(x_(M)) corresponding to the next M magnetizationstate transitions read by the magnetic read head at positions x₁, x₂, .. . , x_(M) (x<x₁<x₂< . . . <x_(M)) in the magnetic medium along the Xdirection, wherein M is at least 1, wherein W(x_(M)) has a shape that isdistinctive and distinguishable from the readback pulse shape of allother magnetization state transitions of the all possible magnetizationstate transitions, and wherein W(x) together with the next M readbackpulse shapes uniquely identify T_(ij)(x);

identifying the magnetization state transition T_(ij)(x) from W(x) ifthe set (T) consists of T_(ij)(x) or from W(x) together with the next Mreadback pulse shapes if the set (T) comprises T_(ij)(x) and the atleast one other magnetization state transition;

displaying and/or recording the identified magnetization statetransition T_(ij)(x).

The present invention provides a structure comprising a multi-layercontinuous magnetic medium comprising a plurality of magnetic layers,each magnetic layer comprising magnetic material continuouslydistributed in an X-Y plane defined by an X direction and a Y directionorthogonal to each other, consecutive magnetic layers separated bynon-magnetic spacer material and distributed along a Z directionorthogonal to the X-Y plane, wherein the plurality of magnetic layerscomprise a first magnetic layer and a second magnetic layer, wherein thefirst magnetic layer and the second magnetic layer have a magnetic easyaxis respectively oriented at a first tilt angle (α₁) and a second tiltangle (α₂) with respect to the X direction, wherein the first magneticlayer and the second magnetic layer have a magnetic hard axisrespectively oriented at a first tilt angle (α₁*) and a second tiltangle (α₂*) with respect to the X direction, wherein (−80≦α₁*≦−10 and−180<α₂*<−90) or (−180<α₁*<−90 and −80≦α₂*≦−10) or (−80≦α₁*≦−10 and−90<α₂*<0) or (−90<α₁*<0 and −80≦α₂*≦−10).

The present invention provides an apparatus comprising a computerprogram product, said computer program product comprising a computerreadable storage medium having a computer readable program code embodiedtherein, said computer readable program code containing instructionsthat when executed by a processor of a computer system implement amethod for writing magnetization states in a multi-layer continuousmagnetic medium comprising a plurality of magnetic layers, each magneticlayer comprising magnetic material continuously distributed in an X-Yplane defined by an X direction and a Y direction orthogonal to eachother, consecutive magnetic layers separated by non-magnetic spacermaterial and distributed along a Z direction orthogonal to the X-Yplane, said method comprising:

selecting a magnetization state [S1; S2] comprising a magnetic state(S1) and a magnetic state (S2) in a first magnetic layer and in a secondmagnetic layer, respectively, of the plurality of magnetic layers,wherein α₁* and α₂* are a first tilt angle and a second tilt angle atwhich a hard axis of the first magnetic layer and the second magneticlayer are respectively oriented with respect to the X direction, andwherein either or both of α₁* and α₂* are in a range of 0 to −90degrees;

determining a write current (I) sufficient to write the magnetizationstate [S1; S2];

issuing a command for applying the write current I to a magnetic writehead moving in the X direction to generate in the first magnetic layerand the second magnetic layer a magnetic field that exceeds a switchingfield of the first magnetic layer and a switching field of the secondmagnetic layer, respectively, said command causing the magnetic writehead to write the magnetization state [S1; S2] by simultaneously writingthe magnetic state S1 in the first magnetic layer and the magnetic stateS2 in the second magnetic layer.

The present invention provides an apparatus comprising a computerprogram product, said computer program product comprising a computerreadable storage medium having a computer readable program code embodiedtherein, said computer readable program code containing instructionsthat when executed by a processor of a computer system implement amethod for reading magnetic state transitions in a two-layer continuousmagnetic medium comprising two magnetic layers, each magnetic layercomprising magnetic material continuously distributed in an X-Y planedefined by an X direction and a Y direction orthogonal to each other,consecutive magnetic layers separated by non-magnetic spacer materialand distributed along a Z direction orthogonal to the X-Y plane, saidmethod comprising:

issuing a first command for reading at a specific location (x) of themedium along the X direction, by a magnetic read head moving in the Xdirection, a readback pulse shape W(x) associated with a magnetizationstate transition T_(ij)(x) from a magnetization state [S1; S2], to amagnetization state [S1; S2]_(j), wherein i and j are each 1, 2, 3, or 4subject to i≠j, wherein S1 and S2 is a magnetic state in a firstmagnetic layer and in a second magnetic layer, respectively, of the twomagnetic layers, wherein the first magnetic layer and the secondmagnetic layer have a magnetic easy axis respectively oriented at afirst tilt angle (α₁) and a second tilt angle (α₂) with respect to the Xdirection, wherein the magnetization state [S1; S2]₁, [S1; S2]₂, [S1;S2]₃, and [S1; S2]₄ respectively corresponds to a state A=[+1,+1], astate B=[−1,−1], a state C=[+1,−1], and a state D=[−1,+1], wherein themagnetic state S1 is respectively +1 or −1 if a magnetization of thefirst layer is oriented at or opposite the angle α₁, wherein themagnetic state S2 is respectively +1 or −1 if a magnetization of thesecond layer is oriented at or opposite the angle α₂, and wherein thefirst magnetic layer and the second magnetic layer have a magnetic hardaxis respectively oriented at a first tilt angle (α₁*) and a second tiltangle (α₂*) with respect to the X direction;

after said reading W(x) resulting from said first command, identifyingfrom W(x), a set (T) of magnetization state transitions, whereineither 1) the set (T) consists of T_(ij)(x) if W(x) has a readback pulseshape that is distinctive and distinguishable from the readback pulseshape of each other state transition of all possible state transitionsso as to uniquely identify T_(i)(x)_(j) or 2) the set (T) comprisesT_(ij)(x) and at least one other state transition of the all possiblestate transitions whose associated readback pulse shape is notdistinctive and distinguishable from the readback pulse shape of W(x);

if the set T comprises T_(ij)(x) and the at least one other statetransition, then issuing a second command for reading, by the magneticread head moving in the X direction, a next M readback pulse shapesdenoted as W(x₁), W(x₂), . . . W(x_(M)) corresponding to the next Mmagnetization state transitions read by the magnetic read head atpositions x₁, x₂, . . . , x_(M) (x<x₁<x₂< . . . <x_(M)) in the magneticmedium along the X direction, wherein M is at least 1, wherein W(x_(M))has a readback pulse shape that is distinctive and distinguishable fromthe readback pulse shape of all other magnetization state transitions ofthe all possible state transitions, and wherein W(x) together with thenext M readback pulse shapes uniquely identify T_(ij)(x);

identifying the magnetization state transition T_(ij)(x) from W(x) ifthe set (T) consists of T_(ij)(x) or from W(x) together with the next Mreadback pulse shapes if the set (T) comprises T_(ij)(x) and the atleast one other state transition;

displaying and/or recording the identified magnetization statetransition T_(ij)(x).

The present invention provides magnetic recording with a continuousrecording medium that allows increased recording density and improvesthe efficiency of writing bits of data on the continuous multi-layerrecording medium.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic description of a multi-layer continuous magneticmedium with 2 layers, in accordance with embodiments of the presentinvention.

FIG. 2 is a representation of magnetic fields generated by a write head,in accordance with embodiments of the present invention.

FIG. 3 depicts a Stoner-Wolfarth astroid representing the amplitude ofswitching field as a function of field direction related to easy axisdirection along +30°, in accordance with embodiments of the presentinvention.

FIGS. 4A, 4B, 4C, 4D, 4E, and 4F show calculations of the write currentfor multi-layered continuous magnetic media for various ranges of hardaxis angle in the top and bottom layers, in accordance with embodimentsof the present invention.

FIGS. 5 a-5 l depict readback pulse shapes of the 12 magnetization statetransitions for a particular example, in accordance with embodiments ofthe present invention.

FIG. 6A depicts a magnetic read head above a magnetic medium, inaccordance with embodiments of the present invention.

FIG. 6B depicts a magnetic write head above a magnetic medium, inaccordance with embodiments of the present invention.

FIG. 6C depicts a magnetic read head above a magnetic medium, inaccordance with embodiments of the present invention.

FIG. 6D depicts a magnetic read/write head above a magnetic medium, inaccordance with embodiments of the present invention.

FIG. 7 depicts the readback pulse shapes of the 12 magnetization statetransitions of FIGS. 5 a-5 i together in one graphical plot, inaccordance with embodiments of the present invention.

FIG. 8 shows the 6 positive readback pulse shapes of the 12 readbackpulse shapes from the 12 magnetization state transitions of FIG. 7, inaccordance with embodiments of the present invention.

FIG. 9 is a schematic description of a multi-layer continuous magneticmedium with more than two layers, in accordance with embodiments of thepresent invention.

FIG. 10 is a flow chart of a method for writing a magnetization state ina multi-layer continuous magnetic medium, in accordance with embodimentsof the present invention.

FIG. 11 is a flow chart of a method for reading magnetization statesfrom a two-layer continuous magnetic medium, in accordance withembodiments of the present invention.

FIG. 12 illustrates a computer system used for executing software toimplement the methodology of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides multi-layer continuous magnetic recordingmedium comprising N layers (N≧2), a method for writing independent bitssimultaneously at two layers of the medium thus reducing the writingsteps for the two layers by a factor of 2. The present invention alsoprovides a method for reading the information states stored insimultaneously written two layers of a two-layer continuous magneticrecording medium. The method and system of the present invention is withrespect to a two-layer magnetic medium (i.e., N=2) or to a selected twolayers of a magnetic medium comprising more than 2 layers (i.e., N>2).

FIG. 1 is a schematic description of a multi-layer continuous magneticmedium 30 with 2 layers, in accordance with embodiments of the presentinvention. FIG. 1 depicts X, Y, and Z axes of a (X, Y, Z) right-handedrectangular coordinate system in which the X, Y, and Z directions aremutually orthogonal to one another. An X direction along the X axis anda Y direction along the Y axis define an X-Y plane. A Z direction alongthe Z axis is orthogonal to the X-Y plane. The magnetic medium 30comprises a recording layer made of a top granular or particulatemagnetic layer 11, a bottom granular or particulate magnetic layer 12, aspacer layer 16 between the top layer 11 and the bottom layer 12, and asubstrate 19. The top layer 11 and the bottom layer 12 each comprisemagnetic material continuously distributed in the X-Y plane. In oneembodiment, the spacer layer 16 does not exist and consecutive magneticlayers stacked along the Z direction are not physically separated fromeach other but nonetheless behave independently. The magnetic medium 30may include an overcoat 17 and an under-layer 18 between the recordinglayer and a substrate 19.

In one embodiment, the substrate 19 may comprise a material used in diskdrives (e.g., conventional disk drives), including a material such as,inter alia, glass and AlMg. In one embodiment, the substrate 19 maycomprise a semiconductor material such as, inter alia, silicon. In oneembodiment, the substrate 19 may be a plastic substrate (e.g., PET, PEN,Aramid) used for tape media.

In one embodiment, the under-layer 18 may include one or more materialscan be used as seeds and for promoting orientation of the magneticlayers and may include, inter alia, Ti, Cr, C, NiAl, CoCr, CoO, etc.

In one embodiment, the overcoat 17 may be, inter alia, a diamond-likecarbon overcoat, a lubricant layer, etc.

The top layer 11 and the bottom layer 12 are parallel to the plane (XY)that includes the X and Y directions and are separated in the Zdirection which is orthogonal to the X direction (see FIG. 1B) by thenon-magnetic layer 16. In one embodiment, the spacer layer 16 comprisesa non-magnetic spacer material such as, inter alia, Cu, Ag, Au, Ru, CoO,SiO, etc. In one embodiment, the spacer layer 16 comprises aferromagnetic material that does not disturb the magnetic behavior ofthe top layer 11 and the bottom layer 12. In another embodiment, the toplayer 11 and the bottom layer 12 are not physically separated from eachother but nonetheless behave independently.

The magnetic material of each top layer 11 and bottom layer 12 maycomprise, inter alia, thin film or particulate, made of Fe, Co, Ni, ormade of an alloy containing at least one element among Fe, Co, Ni, Mn,Cr. Typical media materials are based on: Co alloys (e.g., CoPtCr, CoCo₃Pt); magnetic alloys with L10 phase (e.g., FePd, FePt, CoPt, MnAl),rare earth alloys (e.g., FeNdB, SmCo₅); oxides (e.g., CrO₂, Fe₃O₄,(CoFe)₃O₄, BaFeO).

FIG. 1 depicts an (X, Y, Z) rectangular coordinate system. In theforward direction, the magnetic head (see FIG. 6) is moving in thepositive X direction. In the reverse direction, the magnetic head ismoving in the negative X direction. Any line or vector, as representedby the line 29 in FIG. 1, makes a positive angle with the X axis asshown. Unless otherwise stated, all numerical values of angles appearingherein, including in the claims, are in units of degrees.

FIG. 6A depicts a magnetic read head 31 above the magnetic medium 34,which is analogous to the magnetic medium 30 of FIG. 1, such that theread head 31 is configured to move in the +X or −X direction, inaccordance with embodiments of the present invention. The read head 31,which comprises a magnetoresistive read element 32 and a magnetic shield33 surrounding the magnetoresistive read element 32, is configured toread data from the magnetic medium 34.

FIG. 6B depicts a magnetic write head 35 above a magnetic medium 34, inaccordance with embodiments of the present invention. The write head 35comprises a coil 7 wound around a soft core 6 and configured to carry anelectric current in the coil wire 7 for generating a magnetic field thatextends into the medium 34 and has a field strength exceeding thecoercivity (i.e., switching field) of the medium 34 so as to write datato the magnetic medium 34.

FIG. 6C depicts a magnetic read head 36 above the magnetic medium 34, inaccordance with embodiments of the present invention. The read head 36,which comprises a magnetoresistive read element 37 and a magnetic shield38 surrounding the magnetoresistive read element 37, is configured toread data from the magnetic medium 34.

FIG. 6D depicts a magnetic read/write head 39 above a magnetic medium34, in accordance with embodiments of the present invention. Themagnetic read/write head 39, which comprises the write head 35 of FIG.6B and the read head 36 of FIG. 6C, is configured to both write data toand read data from the magnetic medium 34.

In FIGS. 6A-6D, the read heads 31 and 36 and the write head 35 eachextend along the Y direction.

For the description herein, a magnetic write head is a magnetic headthat is configured to write to, but not to read from, a magnetic medium(e.g., the write head 35 of FIG. 6B or of FIG. 6D). Similarly, amagnetic read head is a magnetic head that is configured to read from,but not write to, a magnetic medium (e.g., the read head 31 of FIG. 6Aor the read head 36 of FIG. 6C or FIG. 6D.

In FIG. 1, the top layer 11 comprises: magnetic material having amagnetic easy axis tilted at an angle α_(t) (−90<α_(t)<90) with respectto the X axis, a magnetic hard axis tilted at an angle α_(t)*(−180<α_(t)*<0) with respect to the X axis, a switching field H_(sw,t),a remanent magnetization M_(r,t), and a thickness T_(t) in the Zdirection. The magnetization 21 in the top layer 11 represents amagnetic state that is oriented along the easy axis, either at the angleα_(t) with respect to the X axis or at the angle 180+α_(t) with respectto the X axis.

The bottom layer 12 comprises magnetic material having a magnetic easyaxis that is tilted at an angle α_(b)* (−90<α_(b)<90) with respect tothe X axis, a magnetic hard axis tilted at an angle α_(b)*(−180<α_(b)*<0) with respect to the X axis, a switching field H_(sw,b),a remanent magnetization M_(r,b), and a thickness T_(b) in the Zdirection. The magnetization 22 in the bottom layer 12 represents amagnetic state in the bottom layer 12 that is oriented along the easyaxis, either at the angle α_(b) with respect to the X axis or at theangle 180+α_(b) with respect to the X axis.

The hard axis tilt angle α_(t)* can be between −80 and −10 degrees.Then, if recording in both +X and −X directions is required, α_(b)*should be between −170 and −100 degrees. Otherwise, α_(b)* can be anyangle given certain conditions that vary with α_(t)*, H_(sw,b)/H_(sw,t)ratio, the medium thicknesses T_(b) in the Z direction, the head-mediaspacing, and the write head characteristics.

The hard axis tilt angle α_(b)* can be between −80 and −10 degrees.Then, if recording in both +X and −X directions is required α_(t)*should be between −170 and −100 degrees. Otherwise, α_(t)* can be anyangle given certain conditions that vary with α_(b)*, H_(sw,b)/H_(sw,t)ratio, the thicknesses T_(b) in the Z direction, the head-media spacing,and the write head characteristics.

The angles α_(t)*, α_(b)*, α_(t), α_(b), of the top layer 11 and thebottom layer 12, the dimensions and thickness T_(t) and T_(b) of the toplayer 11 and the bottom layer 12, the thickness of the spacer layer 16,the magnetic materials of the top layer 11 and the bottom layer 12 andthe switching fields H_(sw,t), H_(sw,b) of the top layer 11 and thebottom layer 12, respectively, can be adjusted for optimum writing,optimum data retention, and such that all four possible magnetizationstates in the medium are differentiated in the readback signal.

Each layer of the magnetic medium 30 can be made of a large assembly ofnanoparticles with a similar easy axis within each layer and anindependent easy axis for each layer. When all nanoparticles are alignedin the same positive direction, and when there is no spacer layer, thedepth of the transition between the top layer 11 and the bottom layer 12can be defined by the write current applied to the magnetic head 35 ofFIG. 6B or of FIG. 6D.

The present invention enables writing the two-layer multi-layer magneticmedium 30 at two depths simultaneously.

With two layers being written, there are 2²=4 possible magnetic statesof the medium at a given X position. Each magnetization state is definedby the orientation of the magnetization M_(r,t) and M_(r,b) in the topand bottom layers, respectively. With +1 corresponding to themagnetization along α_(t) or α_(b), −1 corresponding to themagnetization along 180+α_(t) or 180+α_(b), the 4 magnetization statesare A=[+1,+1], B=[−1;−1], C=[+1,−1], D=[−1,+1]. Thus, the magnetizationstate [S1; S2] represents A, B, C, or D with the first magnetic stateS1=±1 and the second magnetic state S2=±1 defining the magneticorientation of the top layer 11 and the bottom layer 12, respectively.

The magnetization of the top and bottom layers of the medium is setsimultaneously by using an adequate write current applied to themagnetic write head 35 of FIG. 6B or FIG. 6D. For each of the 4recording medium states (A, B, C, D), there is a different writecurrent: I1, I2, −I1 and −I2. These write currents are defined by thewrite head characteristics, the head-media spacing, and the dimensionsand magnetic parameters of the medium (hard axis angles, anisotropyfield values, angular dependence of the switching fields). The writingprocess is described in detail infra.

Writing the two layers simultaneously uses any write head such as aconventional write head (e.g., a conventional ring head). Such a writehead generates magnetic fields in the magnetic medium. The fieldamplitude increases with increasing write current. The field amplitudedecreases with increasing distance from the write gap center to aposition in the medium. The field angle φ (with respect to the X axis)also varies depending on the relative position of the head to the mediumas illustrated in FIG. 2.

FIG. 2 is a representation of magnetic fields generated by a write head,in accordance with embodiments of the present invention. Given aposition (X, Z) in the magnetic medium, X denotes the distance (in theX-direction) between the position (X, Z) in the magnetic medium and atrailing edge of the write head, and Z denotes the distance (in the Zdirection) between the position (X, Z) in the magnetic medium and thewrite head. Arrows 26 represents magnetic field direction and fieldamplitude at given points. Lines 27 are contour plots of the fieldnormalized to the deep gap field Hg (levels going from 0.2 to 1). Lines28 are contour plots of the field angle φ (levels of 0 degree to +/−80degrees). Note that Hg is proportional to the write current I:Hg.g=N.I.ε, with g the write gap, N the number of turns, and ε theefficiency of the head. This is a calculation using Karlqvistapproximation with a write gap g of 200 nm.

A magnetic layer of the medium switches its magnetization when the fieldto which it is submitted is larger than the switching field (H_(sw)) ofthat layer. The value of the switching field depends on the materialproperties of the magnetic layer and of the relative angle between theapplied field and the magnetic layer easy or hard axis direction. Thematerial properties of the magnetic layer is determined by the magneticmedium and defines the anisotropy field H_(a).

If the field (H) generated by the write head is larger than H_(sw)(φ)with α₀*<φ<α₀*+180 then the resulting state is +1 (M along α₀), whereinφ is the angle of magnetic field in the magnetic medium with respect tothe X direction, wherein α₀ denotes the tilt angle, α_(t) or α_(b), ofthe magnetic easy axis in the top layer or the bottom layer,respectively, and wherein α₀* denotes the tilt angle, α_(t)* or α_(b)*,of the magnetic hard axis in the top later or the bottom layer,respectively. In one embodiment, the magnetic material is characterizedby the hard axis angle α₀* being equal to −90+α₀. If the field (H) islarger than H_(sw)(φ) with α₀*−180<φ<α₀*, then the resulting state is −1(M along 180+α₀). FIG. 3 (discussed infra) illustrates this with α₀=30°and Stoner-Wolhfarth modelH_(sw)(φ)=H_(a)/[sin^((2/3))(φ−a₀)+cos^((2/3))(φ−α₀)]^((3/2)) andα₀=α₀*+90 used as an example of the dependence of the switching fieldvs. easy axis angle α₀.

In one embodiment, the magnetic material is characterized by |α₀*−α₀|not being equal to 90 degrees.

FIG. 3 depicts a Stoner-Wolfarth astroid representing the amplitude ofswitching field as a function of field direction related to easy axisdirection along +30°, in accordance with embodiments of the presentinvention. The hard axis angle is −60 ° for that model. For appliedfields between [−60,120] the resulting state after all fields areswitched off is +1 (along 30° direction). For fields between [−240,−60]the resulting state after all fields are switched off is −1 (along −150°direction).

As described supra, the fields created by a write head at the trailingedge have angles φ that vary from 0 to almost −90 degrees (with positivecurrent) depending on the X position (X varying from 0 to −infinity).Moreover, the amplitude of the field decreases if the Z distance to thehead increases and if the X position decreases towards −infinity, but istuned by the write current.

From the discussion supra of FIGS. 2 and 3, the following facts (a),(b), (c), (d), (e) and (f) are deduced.

-   (a) For α_(t)* between −80 and −10 degrees, and α_(b)* between −180    and −90 degrees:

(a1) a positive write current (I1a) may be determined such that in thetop layer 11, α_(t)*<φ_(t)<0 and H_(t)≧H_(sw,t)(φ_(t)) andsimultaneously in the bottom layer 12, α_(b)*<φ_(b)<0 andH_(b)≧H_(sw,b)(φ_(b)), wherein H_(t) and H_(b) respectively denote themagnetic field strength in the top layer 11 and the bottom layer 12, andwherein φ_(t) and φ_(b) respectively denote the magnetic field directionrelative to the X axis in the top layer 11 and the bottom layer 12.Then, after removal of all fields, the magnetization in top layer 11 andbottom layer 12 snaps back on the easy axis along +α_(t) and α_(b)(state A).

(a2) a positive write current (I2a>I1a) may be determined such that: inthe top layer 11, −90 <φ_(t)<α_(t)* and H_(t)≧H_(sw,t)(φ_(t)); and inthe bottom layer 12, α_(b)*<φ_(b)<0 and H_(b)≧H_(sw,b)(φ_(b)). Then,after removal of all fields, the magnetization in both layers 11 and 12snaps back on the easy axis along 180+α_(t) for the top layer 11 andα_(b) for the bottom layer 12 (state D).

(a3) using currents of opposite polarities (−I1a and 'I2a) the medium iswritten in the two other possible medium magnetization states (B and Crespectively).

-   (b) For α_(b)* between −80 and −10 degrees, and α_(t)* between −180    and −90 degrees:

(b1) a positive write current (I 1 b) may be determined such that in thetop layer 11, α_(t)*<φ_(t)<0 and H_(t)≧H_(sw,t)(φ_(t)) andsimultaneously in the bottom layer 12, α_(b)*<φ_(b)<0 andH_(b)≧H_(sw,b)(φ_(b)). Then, after removal of all fields, themagnetization in both layers 11 and 12 snaps back on the easy axis along+α_(t) and −α_(b) (state A).

(b2) a positive write current (I2b>I1b) may be determined such that inthe top layer 11, α_(t)*<φ_(t)<0 and H_(t)≧H_(t)(φ_(t)) and in thebottom layer 12, −90<φ_(b)<α_(b)* and H_(b)≧H_(sw,b)(φ_(b)). Then, afterremoval of all fields, the magnetization in both layers 11 and 12 snapsback on the easy axis along α_(t) for the top layer 11 and 180+α_(b) forthe bottom layer 12 (state C).

(b3) using currents of opposite polarities (−I1b and −I2b) the medium iswritten in the two other possible medium magnetization states (states Band D respectively).

-   c) For or α_(t)* between −80 and −10 degrees, and α_(b)* between −90    and 0 degrees that satisfies α_(b)*<φ_(b)<0 with    H_(b)≧H_(sw,b)(φ_(b)) at I2c everywhere in the bottom layer 12:

(c1) a positive write current (I1c) may be determined such that in thetop layer 11, α_(t)*<φ_(t)<0 and H_(t)≧H_(sw,t)(φ_(t)) andsimultaneously in the bottom layer 12, α_(b)*<φ_(b)<0 andH_(b)≧H_(sw,b)(φ_(b)). Then, after removal of all fields, themagnetization in both layers 11 and 12 back on the easy axis along+α_(t) and +α_(b) (state A).

(c2) a positive write current (I2c>I1c) may be determined such that inthe top layer 11, −90<φ_(t)<α_(t)* and H_(t)≧H_(sw,t)(φ_(t)) and in thebottom layer 12, α_(b)*<φ_(b)<0 and H_(b)≧H_(sw,b)(φ_(b)). Then, afterremoval of all fields, the magnetization in both layers 11 and 12 snapsback on the easy axis along 180+α_(t) for the top layer 11 and α_(b) forthe bottom layer 12 (state D).

(c3) using currents of opposite polarities (−I1c and −I2c) the medium iswritten in the two other possible medium magnetization states (B and Crespectively).

-   d) For α_(b)* between −80 and −10 degrees, and α_(t)* between −90    and 0 degrees that satisfies α_(t)*<φ_(t)<0 and H_(t)≧H_(sw,t) at    I2d everywhere in the top layer 11:

(d1) a positive write current (I1d) may be determined such that in thetop layer 11, α_(t)*<φ_(t)<0 and H_(t)≧H_(sw,t)(φ_(t)) andsimultaneously in the bottom layer 12, α_(b)*<φ_(b)<0 andH_(b)≧H_(sw,b)(φ_(b)). Then, after removal of all fields, themagnetization in both layers 11 and 12 snaps back on the easy axis along+α_(t) and +α_(b) (state A).

(d2) a positive write current (I2d>I1d) may be determined such that inthe top layer 11, α_(t)*<φ_(t)<0 and H_(t)≧H_(sw,t)(φ_(t)) and in thebottom layer 12, −90<φ_(b)<α_(b)* and H_(b)≧H_(sw,b)(φ_(b)). Then, afterremoval of all fields, the magnetization in both layers 11 and 12 snapsback on the easy axis along α_(t) for the top layer 11 and 180+α_(b) forthe bottom layer 12 (state C).

(d3) using currents of opposite polarities (−I1d and −I2d) the medium iswritten in the two other possible medium magnetization states (states Band D respectively).

-   e) For α_(t)* between −80 and −10 degrees, and α_(b)* between −90    and 0 degrees that satisfies α_(b)*<φ_(b)<0 with    H_(b)≧H_(sw,b)(φ_(b)) at I2e everywhere in the bottom layer 12:

(e1) a positive write current (I1e) may be determined such that in thetop layer 11, −90<φ_(t)<α_(t)* and H_(t)≧H_(sw,t)(φ_(t)) andsimultaneously in the bottom layer 12, −90<φ_(b)<α_(b)* andH_(b)≧H_(sw,b)(φ_(b)). Then, after removal of all fields, themagnetization in both layers 11 and 12 back on the easy axis along180+α_(t) and 180+α_(b) (state B).

(e2) a positive write current (I2e<I1e) may be determined such that inthe top layer 11, −90<φ_(t)<α_(t)* and H_(t)≧H_(sw,t)(φ_(t)) and in thebottom layer 12, α_(b)*<φ_(b)<0 and H_(b)≧H_(sw,b)(φ_(b)). Then, afterremoval of all fields, the magnetization in both layers 11 and 12 snapsback on the easy axis along 180+α_(t) for the top layer 11 and α_(b) forthe bottom layer 12 (state D).

(e3) using currents of opposite polarities (−I1e and −I2e) the medium iswritten in the two other possible medium magnetization states (A and Crespectively).

-   f) For α_(b)* between −80 and −10 degrees, and α_(t)* between −90    and 0 degrees that satisfies α_(t)*<φ_(t)<0 and    H_(t)≧H_(sw,t)(φ_(t)) at I2f everywhere in the top layer 11:

(f1) a positive write current (I1f) may be determined such that in thetop layer 11, −90<φ_(t)<α_(t)* and H_(t)≧H_(sw,t)(φ_(t)) andsimultaneously in the bottom layer 12, −90<φ_(b)<α_(b)* andH_(b)≧H_(sw,b)(φ_(b)). Then, after removal of all fields, themagnetization in both layers 11 and 12 back on the easy axis along180+α_(t) and 180+α_(b) (state B).

(f2) a positive write current (I2f<I1f) may be determined such that inthe top layer 11, α_(t)*<φ_(t)<0 and H_(t)≧H_(sw,t)(φ_(t)) and in thebottom layer 12, −90<φ_(b)<α_(b)* and H_(b)≧H_(sw,b)(φ_(b)). Then, afterremoval of all fields, the magnetization in both layers 11 and 12 snapsback on the easy axis along α_(t) for the top layer 11 and 180+α_(b) forthe bottom layer 12 (state C).

(f3) using currents of opposite polarities (−I1f and −I2f) the medium iswritten in the two other possible medium magnetization states (states Aand D respectively).

In one embodiment, α_(t)≠α_(b).

In one embodiment, |α_(t)|≠|a_(b)|.

In one embodiment, −80≦α_(t)*≦−10 and −180<α_(b)*<−90.

In one embodiment, −180<α_(t)*<−90 and −80≦α_(b)*≦−10.

In one embodiment, −80≦α_(t)*≦−10 and −90<α_(b)*<0.

In one embodiment, −90<α_(t)*<0 and −80≦α_(b)*≦−10.

FIGS. 4A, 4B, 4C, 4D, 4E, and 4F (collectively, “FIG. 4”) show acalculation of the write current (I1 and I2) for the multi-layercontinuous magnetic media for various ranges of hard axis angle in thetop and bottom layers, in accordance with embodiments of the presentinvention. In FIG. 4, the magnetic medium comprises 30 nm thick top andbottom layers, a 10 nm thick spacer layer, a head-media spacing of 30nm, and a write gap of 200 nm. Karlqvist head fields have been used tocalculate the stray field from the write head. In FIG. 4, the deep gapfield (which is directly proportional to the write current) isnormalized to the anisotropy fields of each layer. Each layer can havedifferent anisotropy fields. The calculation of I1 and I2 write currentsor corresponding deep-gap fields (normalized to each layer anisotropyfield) allow the top and bottom layer of the medium to be writtenindependently as a function of the hard angle absolute value of α_(t)*(solid lines) and α_(b)* (dotted lines). In FIG. 4A, α_(t)* is between−80 and −10 degrees, and α_(b)* is between −180 and −90 degrees. In FIG.4B, α_(b)* is between −80 and −10 degrees, and α_(t) is between −180 and−90 degrees. In FIG. 4C, α_(t)* is between −80 and −10 degrees, andα_(b)* is between −90 and 0 degrees. In FIG. 4D, α_(b)* is between −80and −10 degrees, and α_(t)* is between −90 and 0 degrees. In FIG. 4E,α_(t)* is between −80 and −10 degrees, and α_(b)* is between −90 and 0degrees. In FIG. 4F, α_(b)* is between −80 and −10 degrees, and α_(t)*is between −90 and 0 degrees.

With respect to forward and backward recording directions, if α_(t)* isbetween −80 and −10 degrees, and α_(b)* is between −170 and −100degrees, then the two-level medium can be written simultaneously at thetwo depths of the medium and independently of the recording direction.In the forward direction (head moving in the +X direction), the mediumis written into the A, B, C, or D magnetization state using current I1a,I2a, −I1a or −I2a. In the backward direction (head moving in the −Xdirection), the angles are reversed and the 4 data magnetization statesare written using current I1b, I2b, −I1b and −I2b.

Additionally with respect to forward and backward recording directions,if α_(t)* is between −170 and −100 degrees, and α_(b)* is between −80and −10 degrees, then the two-level medium can be written simultaneouslyat the two levels of the medium and independently of the recordingdirection. In the forward direction (head moving in the +X direction),the medium is written into the A, B, C, or D magnetization state usingcurrent I1b, I2b, −I1b or −I2b. In the backward direction (head movingin the −X direction), the angles are reversed and the 4 magnetizationstates are written using current I1a, I2a, −I1a and −I2a.

For reading two levels of bits of the medium, the magnetic read head 31in FIG. 6A (or the magnetic read head 36 of FIG. 6C or FIG. 6D) performsreading such as by using a conventional reading sensor (e.g., amagnetoresistive head) that passes above the medium at a given velocityand with a given head-media spacing.

The readback pulse shape actually measures a transition betweenconsecutive magnetization states [S1, S2] at a position X₁₂ in the mediaalong the X axis, such that right before the transition position X₁₂ themedia is written in the magnetization state S1 and right after thetransition position X₁₂ the media is written in the magnetization stateS2. The four magnetization states (A, B, C, D) that can be written inthe media corresponds 12 different transitions (a)-(l) corresponding tothe preceding transition as depicted infra in Table 1

Table 1 depicts the 12 different magnetization state transitions thatcan be written in the medium as combinations of magnetizations (α_(t),α_(b), 180+α_(t), 180+α_(b)) for each layer, using currents I1, I2, −I1,and −I2. The 12 magnetization state transitions are denoted astransitions (a), (b), (c), (d), (e), (f), (g), (h), (i), (j), (k), and(l). For example, transition (d) is a transition from magnetizationstate A (+1/+1) triggered by current +I1 to magnetization state C(+1,−1) triggered by current −I2.

TABLE 1 To A (+1/+1) C (+1/−1) D (−1/+1) B (−1/−1) From (+I1) (−I2)(+I2) (−I1 ) A (+1/+1) — (d) A to C (c) A to D (e) A to B (+I1) C(+1/−1) (g) C to A — (f) C to D (h) C to B (−I2) D (−1/+1) (l) D to A(a) D to C — (b) D to B (+I2) B (−1/−1) (j) B to A (k) B to C (i) B to D— (−I1)

FIGS. 5 a-5 l (collectively, “FIG. 5”) depict the 12 magnetization statetransitions (a)-(l), respectively, of Table 1 for a particular example,in accordance with embodiments of the present invention. Themagnetization state transitions in FIG. 5 are characterized by:α_(t)=+30° and α_(b)=−30°, α_(t)*=60° and α_(b)*=−120°, with sameanisotropy field H_(a,t)=H_(a,b) for the top and bottom layers, T_(t)=30nm, T_(b)=30 nm, 10 nm thick spacer, a head-media spacing of 30 nm and awrite gap of 200 nm. Then I1 can be 1.17.H_(a,t) and I2 can be2.H_(a,t).

For each magnetization state transition in FIG. 5, graphs labeled “W.Current”, “M in media”, and “Norm Read” are shown. “W. Current” is thewrite current (±I₁, ±I₂) as a function of the position (X) of the writemagnetic head above the medium. “M in media” denotes the magnetizationstate (±1) in the top layer and in the bottom layer in the medium asindicated in the legend. “Norm Read” is the readback pulse shape (afterbeing normalized to fall within ±1) for the magnetization statetransition.

For reading two layers of bits of the continuous medium, the magneticread head 31 in FIG. 6 (or the magnetic read head 36 of FIG. 6C or FIG.6D) performs reading such as by using a conventional reading sensor(e.g., a magnetoresistive head) that passes above the medium at a givenvelocity and with a given head-media spacing.

FIG. 7 depicts the readback pulse shapes of the 12 magnetization statetransitions of FIG. 5 together in one graphical plot, in accordance withembodiments of the present invention. These readback pulse shapes aresymmetric by pairs (positive pulse and negative pulse).

FIG. 8 shows the 6 positive readback pulse shapes of the 12 readbackpulse shapes from the 12 magnetization state transitions of FIG. 7, inaccordance with embodiments of the present invention.

Four out of the six different positive readback pulse shapes aredistinctive from one another. These are the pulse shapes correspondingto the magnetization state transitions (f), (d), (b), (e). The readbackpulse shapes corresponding to the magnetization state transitions (c)and (h) are, however, very similar and cannot be easily differentiated.This is because there is no transition in the bottom layer of the mediumand there is the same transition in the top layer (see FIG. 5,transition states (c) and (h)). Since there is almost no contribution tothe pulse shape from the medium when no transitions are present, it isthus not a surprise that transitions (c) and (h) present the same pulseshape. Magnetization state transitions (b) and (d) should also be verysimilar for the same reason, namely that there is no transition in thetop layer of the medium but the same transition in the top layer (seeFIG. 5, transitions (b) and (d)). For transition (b), however, there isa small reversed domain due to the rapid variation of write current fromvery high I2 to low write current I1. As a result, the readback pulseshapes corresponding to the transitions (b) and (d) are distinguishablealthough relatively close in amplitude and shape.

To resolve the ambiguity between the transitions (c) and (h), it isnecessary to consider the next transition state in the media, along theread direction X. The next transition after transition (c) isnecessarily (a), or (b), or (l), and the next transition aftertransition (h) is necessarily (i), or (j), or (k). The pulse shape formagnetization state transition (a), (b), (i), or (j), are easilydistinguishable from each other. Therefore, the ambiguity betweentransition (c) and (h) can be resolved when the following transition is(a), (b), (i) or (j). Otherwise, it is not possible to resolve theambiguity between transition (c) and (h) because the transition (l) andthe transition (k) also have similar readback pulse shapes. In thatparticular case, it is necessary to consider as well the next transitionto decode the written data. Similarly the transition after transition(l), is necessarily (f), or (g), or (c), and the transition aftertransition (k), is necessarily (d), or (e), or (h). The readback pulseshape for magnetization state transition (f), (g), (d) and (e) areeasily distinguishable from each other. Therefore, the ambiguity betweentransition (l) and (k) is resolved when the next detected readback pulseshape corresponds to the transition state (f), (g), (d) or (e). In turn,the ambiguity between (c) and (h) from the previous transition is alsoreleased. In the two other cases, (l) and (k) being followed by (c) and(h) respectively, it is not possible to resolve the ambiguity between(l) and (k). In that particular case, it is necessary to consider thenext transition.

This decoding scheme can be applied for several consecutive transitions.The ambiguity between the sequence of transitions . . . (c)-(l)-(c)-(l). . . and the sequence of transition . . . (h)-(k)-(h)-(k) . . . isresolved as soon as the transition (c) is not followed by the transition(l), or the transition (l) is not followed by the transition (c), or thetransition (h) is not followed by the transition (k), or the transition(k) is not followed by the transition (l). Coding during write can beused to prevent too long magnetization state transition sequences . . .(l)-(c)-(l)-(c) . . . or . . . (h)-(k)-(h)-(k) . . . . If required thistechnique may be applied in a similar fashion for magnetization statetransitions (b) and (d) and their symmetrical counterparts: transitions(g) and (l).

Thus, different magnetization combinations with two levels can all bedistinguished by the pulse shape of the transition or by the pulse shapeof the transition and that of the next transitions. This can be includedinto adapted readback channel and data encoding.

The preceding example presented supra in conjunction with FIGS. 5, 7,and 8 is an illustrative example. The amplitude level and the shape ofeach of these readback pulse shapes can be optimized by the design ofthe magnetic medium 30 (see FIG. 1) and also depends on the write headand read head characteristics.

In the preceding example, an ambiguity in a first magnetization statestransition was resolved by considering the next transition. Moregenerally, resolving an ambiguity in a first transition may requireconsidering at least one next transition, such as the next twotransitions, the next three transitions, etc., depending on the extentto which different readback pulse shapes are distinguished from eachother, which in turn depends on the design of the magnetic medium 30(see FIG. 1) and on the write head and read head characteristics.

For a 2-layer continuous magnetic medium described supra, the method ofthe present invention writes magnetic states of the two layerssimultaneously, thus allowing recording with doubled capacity in asingle writing step. The method of the present invention enablesdetermination of magnetic state transitions between written magneticstates by decoding readback pulse shapes specific to the magnetic statetransitions.

FIG. 9 is a schematic description of a multi-layer continuous magneticmedium 50 with N layers such that N is an integer of at least 2, inaccordance with embodiments of the present invention. The magneticmedium 50 comprises recording layers 41, each layer 41 being a granularor particulate magnetic layer. The layers may be separated by a spacerlayer 16. The magnetic medium 50 may include an overcoat 17, and anunder-layer 18 between the recording layers 41 and a substrate 19.

The N magnetic layers 41 are isolated from each other by a spacer layer16. Each layer 41 is a single-domain particle or an assembly ofparticles that behave as a single magnetic volume. A pair of layers 41can be written in a single write step as described supra, resulting in areduction in writing steps by a factor of 2 in comparison with existingwriting methods. For cases of N>2, the two layers in the pair of layers41 may be any two layers of the N layers and are not required to be twophysically consecutive layers (i.e., two neighboring layers with noother layer disposed therebetween).

In one embodiment, N is an even or odd integer of at least 2.

At least one layer of the pair of layers has a hard axis angle between−90 and 0 degrees.

FIG. 10 is a flow chart of a method for writing magnetization states ina multi-layer continuous magnetic medium, in accordance with embodimentsof the present invention. The magnetic medium comprises N magneticlayers oriented in an X direction and extending in a Y direction. Thelayers are distributed in a Z direction, wherein the X, Y, and Zdirections are mutually orthogonal. Consecutive magnetic layers areseparated by spacer material (e.g., non-magnetic spacer material). Themethod of FIG. 10 comprises steps 61-63.

Step 61 selects a magnetization state [S1; S2] comprising a magneticstate (S1) in a first magnetic layer of the N magnetic layers and amagnetic state (S2) in a second magnetic layer of the N magnetic layers,wherein N is at least 2.

Step 62 determines a write current (I) sufficient to write themagnetization state [S1; S2] from a relationship (R) involving α₁*, α₂*,H₁, H₂, φ₁ and φ₂, wherein H₁ and H₂ respectively denote a magneticfield strength in the first magnetic layer and the second magneticlayer, wherein φ₁ and φ₂ respectively denote a magnetic field angle withrespect to the X direction in the first magnetic layer and the secondmagnetic layer, and wherein α₁* and α₂* are a first tilt angle and asecond tilt angle at which a magnetic hard axis of the first magneticlayer and the second magnetic layer are respectively oriented withrespect to the X direction.

The magnetization state [S1; S2] is a state A=[+1,+1], a stateB=[−1,−1], a state C=[+1,−1], or a state D=[−1,+1], wherein the magneticstate S1 is respectively +1 or −1 if a magnetization of the firstmagnetic layer is oriented along its easy axis, at or opposite to theangle α₁ with respect to the X direction, and wherein the magnetic stateS2 is respectively +1 or −1 if a magnetization of the second magneticlayer is oriented along its easy axis at or opposite to the angle α₂with respect to the X direction.

Step 63 applies the write current I to a magnetic write head moving inthe X direction to generate in the first magnetic layer and in thesecond magnetic layer the magnetic fields H₁ and H₂ respectively,oriented at the field angle φ₁ and φ₂ respectively, resulting in writingthe magnetization state [S1; S2] by simultaneously writing the magneticstate S1 in the first magnetic layer and the magnetic state S2 in thesecond magnetic layer.

The write current I will write the magnetization state [S1; S2] in thefirst and second layer of the N layers as described supra for step 63.If N>2, the write current I may also write the remaining (N-2) layers ofthe N layers in a manner that depends on the magnetic properties of theremaining (N-2) layers of the N layers. In one embodiment, the remaining(N-2) layers are not being used and their magnetic states are of noconcern while the magnetization state [S1; S2] is being written in thefirst and second layers, so that it does not matter in this embodimentwhat is specifically written in the remaining (N-2) layers. What may bewritten in the remaining (N-2) layers will contribute to the uniquetransition signal of the magnetization state [S1; S2]_(x) and [S1;S2]_(x+1). This readback pulse shape will necessarily be different tothe readback pulse shapes corresponding to the other combination ofmagnetization states.

In one embodiment, steps 61-63 may be implemented in software via thecomputer system 90 of FIG. 12. The software selects the magnetizationstate [S1; S2] in step 61, executes determining the write current I instep 62, and executes issuing a command for applying the write current Ito the magnetic write head in step 63 which causes the magnetic writehead to write the magnetization state [S1; S2] by simultaneously writingthe magnetic state S1 in the first magnetic layer and the magnetic stateS2 in the second magnetic layer.

FIG. 11 is a flow chart of a method for reading magnetization statesfrom a two-layer continuous magnetic medium, in accordance withembodiments of the present invention. The magnetic medium comprises twomagnetic layers distributed in a Z direction orthogonal to the X-Y planeof the layers. Consecutive magnetic layers may be separated by spacermaterial (e.g., non-magnetic spacer material). The method of FIG. 11comprises steps 71-76.

Step 71 reads, by a magnetic read head moving in the X direction, areadback pulse shape W(x) associated with a magnetization statetransition T_(ij)(x) corresponding to a transition at a defined location(x) along the X axis on the magnetic medium 30 from a firstmagnetization state that includes [S1; S2], to the next magnetizationstate that includes [S1; S2]_(j), wherein i and j are each 1, 2, 3, or 4subject to i≠j. S1 is a magnetic state in a first magnetic layer of thetwo magnetic layers and S2 is a magnetic state in a second magneticlayer of the two magnetic layers. The first magnetic layer and thesecond magnetic layer have a magnetic easy axis respectively oriented ata first tilt angle (α₁) and a second tilt angle (α₂) with respect to theX direction. The magnetization state [S1; S2]₁, [S1; S2]₂, [S1; S2]₃,and [S1; S2]₄ respectively consists of a state A=[+1,+1], a stateB=[−1,−1], a state C=[+1,−1], and a state D=[−1,+1]. The magnetic stateS1 is respectively +1 or −1 if a magnetization of the first layer isoriented at or opposite the angle α₁ with respect to the X direction.The magnetic state S2 is respectively +1 or −1 if a magnetization of thesecond layer is oriented at or opposite the angle α₂ with respect to theX direction. The first magnetic layer and the second magnetic layer havea magnetic hard axis respectively oriented at a first tilt angle (α₁*)and a second tilt angle (α₂*) with respect to the X direction. At leastone tilt angle of the two tilt angles (α₁*) and (α₂*) is between −90 and0 degrees.

Step 72 identifies, from the readback pulse shape W(x) that was read instep 71, a set (T) of magnetization state transition that correspond tothe pulse shape W_(ij)(x). Either the set (T) consists of T_(ij)(x ) ifW(x) has a pulse shape that is distinctive and distinguishable from apulse shape of each other state transition of all possible magnetizationstate transitions so as to uniquely identify T_(ij)(x) or the set (T)comprises T_(ij)(x) and at least one other magnetization statetransition of all possible magnetization state transitions whoseassociated pulse shape is not distinctive and distinguishable from thepulse shape of W(x). Said all possible magnetization state transitionsare a function of the design of the magnetic medium 30 (see FIG. 1) andof the write head and read head characteristics.

Step 73 determines whether the set (T) consists of T_(ij)(x) orcomprises at least one other state transition. If step 73 determinesthat the set (T) consists of T_(ij)(x) (or does not comprises the atleast one other state transition) then step 75 is next executed;otherwise step 74 is next executed.

Step 74 reads, by the magnetic read head moving in the X direction, anext M readback pulse shapes denoted as W(x₁), W(x₂), . . . , W(x_(M))corresponding to the next M magnetization state transitions read by themagnetic read head at positions x₁, x₂, . . . , x_(M) (x<x₁<x₂< . . .<x_(M)) along the X axis in the magnetic medium 30, wherein M is atleast 1. W(x_(M)) has a shape that is distinctive and distinguishablefrom the pulse shape of all other magnetization state transition of theall possible magnetization state transitions. The readback pulse shapeW(x) together with the next M readback pulse shapes uniquely identifiesT_(ij)(x).

Step 75 identifies the magnetization state transition T_(ij)(x) fromW(x) if the set (T) consists of T_(ij)(x) or from W(x) together with thenext M readback pulse shapes if the set (T) comprises T_(ij)(x) and theat least one other state transition.

Step 76 displays and/or records the magnetization state transitionT_(ij)(x) identified in step 75. For example, the uniquely identifiedmagnetization state transition T_(ij)(x) may be displayed on a displaydevice of the computer system 12 of FIG. 12 and/or recorded (i.e.,written) in a memory device of the computer system 90 of FIG. 12.

In one embodiment, steps 71-76 may be implemented in software via thecomputer system 90 of FIG. 12. The software issues a command forreading, by the magnetic read head, the readback pulse shape W(x) instep 71 (which causes the magnetic read head to read the pulse shapeW(x)), identifies the set (T) in step 72, determines whether the set (T)consists of T_(ij)(x) in step 73, issues a command for reading, by themagnetic read head, the Next M pulse shapes in step 74, identifiesT_(ij)(x) in step 75, and displays and/or records T_(ij)(x) in step 76.

FIG. 12 illustrates a computer system 90 used for executing software toimplement the methodology of the present invention. The computer system90 comprises a processor 91, an input device 92 coupled to the processor91, an output device 93 coupled to the processor 91, and memory devices94 and 95 each coupled to the processor 91. The input device 92 may be,inter alia, a keyboard, a mouse, etc. The output device 93 may be atleast one of, inter alia, a printer, a plotter, a computer screen, amagnetic tape, a removable hard disk, a floppy disk, etc. The memorydevices 94 and 95 may be at least one of, inter alia, a hard disk, afloppy disk, a magnetic tape, an optical storage such as a compact disc(CD) or a digital video disc (DVD), a random access memory (RAM), adynamic random access memory (DRAM), a read-only memory (ROM), etc. Thememory device 95 includes a computer code 97. The computer code 97comprises software to implement the methodology of the presentinvention. The processor 91 executes the computer code 97. The memorydevice 94 includes input data 96. The input data 96 includes inputrequired by the computer code 97. The output device 93 stores ordisplays output from the computer code 97. Either or both memory devices94 and 95 (or one or more additional memory devices not shown in FIG.12) may be used as a computer usable storage medium (or a computerreadable storage medium or a program storage device) having a computerreadable program code embodied therein and/or having other data storedtherein, wherein the computer readable program code comprises thecomputer code 97. Generally, a computer program product (or,alternatively, an article of manufacture) of the computer system 90 maycomprise said computer usable storage medium (or said program storagedevice).

In one embodiment, an apparatus of the present invention comprises thecomputer program product. In one embodiment, an apparatus of the presentinvention comprises the computer system such that the computer systemcomprises the computer program product.

While FIG. 12 shows the computer system 90 as a particular configurationof hardware and software, any configuration of hardware and software, aswould be known to a person of ordinary skill in the art, may be utilizedfor the purposes stated supra in conjunction with the particularcomputer system 90 of FIG. 12. For example, the memory devices 94 and 95may be portions of a single memory device rather than separate memorydevices.

While particular embodiments of the present invention have beendescribed herein for purposes of illustration, many modifications andchanges will become apparent to those skilled in the art. Accordingly,the appended claims are intended to encompass all such modifications andchanges as fall within the true spirit and scope of this invention.

1. A method for reading magnetic state transitions in a two-layercontinuous magnetic medium comprising two magnetic layers, each magneticlayer comprising magnetic material continuously distributed in an X-Yplane defined by an X direction and a Y direction orthogonal to eachother, said two magnetic layers separated by non-magnetic spacermaterial and distributed along a Z direction orthogonal to the X-Yplane, said method comprising: reading at a specific location (x) of themedium along the X direction, by a magnetic read head moving in the Xdirection, a readback pulse shape W(x) associated with a magnetizationstate transition T_(ij)(x) from a magnetization state [S1; S2]_(i), to amagnetization state [S1; S2]_(j), wherein i and j are each 1, 2, 3, or 4subject to i≠j, wherein S1 and S2 is a magnetic state in a firstmagnetic layer and in a second magnetic layer, respectively, of the twomagnetic layers, wherein the first magnetic layer and the secondmagnetic layer have a magnetic easy axis respectively oriented at afirst tilt angle (α₁) and a second tilt angle (α₂) with respect to the Xdirection, wherein the magnetization state [S1; S2]₁, [S1; S2]₂, [S1;S2]₃, and [S1; S2]₄ respectively corresponds to a state A=[+1,+1], astate B=[−1,−1], a state C=[+1,−1], and a state D=[−1,+1], wherein themagnetic state S1 is respectively +1 or −1 if a magnetization of thefirst layer is oriented at or opposite the angle α₁, wherein themagnetic state S2 is respectively +1 or −1 if a magnetization of thesecond layer is oriented at or opposite the angle α₂, wherein themagnetic states S1 and S2 are independent of each other, wherein thefirst magnetic layer and the second magnetic layer have a magnetic hardaxis respectively oriented at a first tilt angle (α₁*) and a second tiltangle (α₂*) with respect to the X direction, wherein both α₁* and α₂*differ from 0, 90, 180 and 270 degrees, and wherein −90<α₁*<0 and/or−90<α₂*<0; after said reading W(x), identifying from W(x), a set (T) ofmagnetization state transitions, wherein either 1) the set (T) consistsof T_(ij)(x) if W(x) has a pulse shape that is distinctive anddistinguishable from the readback pulse shape of each othermagnetization state transition of all possible magnetization statetransitions so as to uniquely identify T_(ij)(x) or 2) the set (T)comprises T_(ij)(x) and at least one other magnetization statetransition of the all possible magnetization state transitions whoseassociated readback pulse shape is not distinctive and distinguishablefrom the readback pulse shape of W(x); if the set T comprises T_(ij)(x)and the at least one other magnetization state transition, then reading,by the magnetic read head moving in the X direction, a next M readbackpulse shapes denoted as W(x₁), W(x₂), . . . W(x_(M)) corresponding tothe next M magnetization state transitions read by the magnetic readhead at positions x₁, x₂, . . . , x_(M) (x<x₁<x₂< . . . <x_(M)) in themagnetic medium along the X direction, wherein M is at least 1, whereinW(x_(M)) has a shape that is distinctive and distinguishable from thereadback pulse shape of all other magnetization state transitions of theall possible magnetization state transitions, and wherein W(x) togetherwith the next M readback pulse shapes uniquely identify T_(ij)(x);identifying the magnetization state transition T_(ij)(x) from W(x) ifthe set (T) consists of T_(ij)(x) or from W(x) together with the next Mreadback pulse shapes if the set (T) comprises T_(ij)(x) and the atleast one other magnetization state transition; displaying and/orrecording the identified magnetization state transition T_(ij)(x). 2.The method of claim 1, wherein the set T consists of T_(ij)(x).
 3. Themethod of claim 1, wherein the set T comprises T_(ij)(x) and the atleast one other magnetization state transition.
 4. The method of claim1, wherein (−80≦α₁*≦−10 and −180<α₂*<−90) or (−180<α₁*<−90 and−80≦α₂*≦−10).
 5. The method of claim 1, wherein (−80≦α₁*≦−10 and−90<α₂*<0) or (−90<α₁*<0 and −80≦α₂*≦−10).
 6. The method of claim 1,wherein |α₁|≠|α₂|.
 7. The method of claim 1, and wherein α₁, α₂, or bothα₁ and α₂ is less than 0 degrees and greater than −90 degrees.
 8. Themethod of claim 1, wherein for k=i and k=j, the magnetization state [S1;S2]₁, is generated by a magnetic write head moving in the X direction,said write head generating in the continuous medium a magnetic fieldoriented at a field angle φ₁ and φ₂ with respect to the X direction inthe first magnetic layer and the second magnetic layer, respectively;wherein α₁, α₂, φ₁, and φ₂ satisfy a relationship (R) selected from thegroup consisting of a relationship R1 a, a relationship R1 b, arelationship R1 c, a relationship R1 d, a relationship R1 e, arelationship R1 f, a relationship R2 a, a relationship R2 b, arelationship R2 c, a relationship R2 d, a relationship R2 e, and arelationship R2 f; wherein if [S1; S2] _(k) is A or B, then R is R1 a,R1 b, R1 c, R1 d, R1 e, or R1 f; wherein if [S1; S2] _(k) is C or D,then R is R2 a, R2 b, R2 c, R2 d, R2 e, or R2 f; said relationship R1 ais −80≦α₁*≦−10, α₁*<α₁<0, −180<α₂*<−90, α₂*<φ₂<0; said relationship R2 ais −80≦α₁*≦−10, −90<φ₁<α₁*, −180<α₂*<−90, α₂*<φ₂<0; said relationship R1b is −180<α₁*<−90, α₁*<φ₁<0, −80≦α₂*≦−10, α₂*<φ₂<0; said relationship R2b is −180<α₁*<−90, α₁*<φ₁<0, −80≦α₂*≦−10, −90<φ₂<α₂*; said relationshipR1 c is −80≦α₁*≦−10, α₁*<φ₁<0, −90<α₂*<0, α₂*<φ₂<0; said relationship R2c is −80≦α₁*≦−10, −90<φ₁<α₁*, −90<α₂*<0, α₂*<0₂<0; said relationship R1d is −90<α₁*<0, α₁*<φ₁<0, −80≦α₂*≦−10, α₂*<φ₂<0; said relationship R2 dis −90<α₁*<0, α₁*<φ₁<0, −80≦α₂*≦−10, −90<φ₂<α₂*; said relationship R1 eis −80≦α₁*≦−10, −90<φ₁<α₁*, −90<α₂*<0, −90<φ₂<α₂*; said relationship R2e is −80≦α₁*≦−10, −90<φ₁<α₁*, −90<α₂*<0, α₂*<φ₂<0; said relationship R1f is −90<α₁*<0, −90<φ₁<α₁*, −80≦α₂*≦−10, −90<φ₂<α₂*; said relationshipR2 f is −90<α₁*<0, α₁*<φ₁<0, −80≦α₂*≦−10, −90<φ₂<α₂*.
 9. A computerprogram product, said computer program product comprising a computerreadable storage device having a computer readable program code storedtherein, said computer readable program code containing instructionsthat when executed by a processor of a computer system implement amethod for reading magnetic state transitions in a two-layer continuousmagnetic medium comprising two magnetic layers, each magnetic layercomprising magnetic material continuously distributed in an X-Y planedefined by an X direction and a Y direction orthogonal to each other,said two magnetic layers separated by non-magnetic spacer material anddistributed along a Z direction orthogonal to the X-Y plane, said methodcomprising: reading at a specific location (x) of the medium along the Xdirection, by a magnetic read head moving in the X direction, a readbackpulse shape W(x) associated with a magnetization state transitionT_(ij)(x )from a magnetization state [S1; S2], to a magnetization state[S1; S2]_(i), wherein i and j are each 1, 2, 3, or 4 subject to i≠j,wherein S1 and S2 is a magnetic state in a first magnetic layer and in asecond magnetic layer, respectively, of the two magnetic layers, whereinthe first magnetic layer and the second magnetic layer have a magneticeasy axis respectively oriented at a first tilt angle (α₁) and a secondtilt angle (α₂) with respect to the X direction, wherein themagnetization state [S1; S2]₁, [S1; S2]₂, [S1; S2]₃, and [S1; S2]₄respectively corresponds to a state A=[+1,+1], a state B=[−1,−1], astate C=[+1,−1], and a state D=[−1,+1], wherein the magnetic state S1 isrespectively +1 or −1 if a magnetization of the first layer is orientedat or opposite the angle α₁, wherein the magnetic state S2 isrespectively +1 or −1 if a magnetization of the second layer is orientedat or opposite the angle α₂, wherein the magnetic states S1 and S2 areindependent of each other, wherein the first magnetic layer and thesecond magnetic layer have a magnetic hard axis respectively oriented ata first tilt angle (α₁*) and a second tilt angle (α₂*) with respect tothe X direction, wherein both α₁* and α₂* differ from 0, 90, 180 and 270degrees, and wherein −90<α₁*<0 and/or −90<α₂*<0; after said readingW(x), identifying from W(x), a set (T) of magnetization statetransitions, wherein either 1) the set (T) consists of T_(ij)(x) if W(x)has a pulse shape that is distinctive and distinguishable from thereadback pulse shape of each other magnetization state transition of allpossible magnetization state transitions so as to uniquely identifyT_(ij)(x) or 2) the set (T) comprises T_(ij)(x) and at least one othermagnetization state transition of the all possible magnetization statetransitions whose associated readback pulse shape is not distinctive anddistinguishable from the readback pulse shape of W(x); if the set Tcomprises T_(ij)(x) and the at least one other magnetization statetransition, then reading, by the magnetic read head moving in the Xdirection, a next M readback pulse shapes denoted as W(x₁), W(x₂), . . .W(x_(M)) corresponding to the next M magnetization state transitionsread by the magnetic read head at positions x₁, x₂, . . . , x_(M)(x<x₁<x₂< . . . <x_(M)) in the magnetic medium along the X direction,wherein M is at least 1, wherein W(x_(M)) has a shape that isdistinctive and distinguishable from the readback pulse shape of allother magnetization state transitions of the all possible magnetizationstate transitions, and wherein W(x) together with the next M readbackpulse shapes uniquely identify T_(ij)(x); identifying the magnetizationstate transition T_(ij)(x) from W(x) if the set (T) consists ofT_(ij)(x) or from W(x) together with the next M readback pulse shapes ifthe set (T) comprises T_(ij)(x) and the at least one other magnetizationstate transition; displaying and/or recording the identifiedmagnetization state transition T_(ij)(x).
 10. The computer programproduct of claim 9, wherein the set T consists of T_(ij)(x).
 11. Thecomputer program product of claim 9, wherein the set T comprisesT_(ij)(x) and the at least one other magnetization state transition. 12.The computer program product of claim 9, wherein |α₁|≠|α₂|.
 13. Acomputer system comprising a processor and a computer readable memoryunit coupled to the processor, said memory unit containing instructionsconfigured to be executed by the processor to implement a method forreading magnetic state transitions in a two-layer continuous magneticmedium comprising two magnetic layers, each magnetic layer comprisingmagnetic material continuously distributed in an X-Y plane defined by anX direction and a Y direction orthogonal to each other, said twomagnetic layers separated by non-magnetic spacer material anddistributed along a Z direction orthogonal to the X-Y plane, said methodcomprising: reading at a specific location (x) of the medium along the Xdirection, by a magnetic read head moving in the X direction, a readbackpulse shape W(x) associated with a magnetization state transitionT_(ij)(x) from a magnetization state [S1; S2], to a magnetization state[S1; S2]_(j), wherein i and j are each 1, 2, 3, or 4 subject to i≠j,wherein S1 and S2 is a magnetic state in a first magnetic layer and in asecond magnetic layer, respectively, of the two magnetic layers, whereinthe first magnetic layer and the second magnetic layer have a magneticeasy axis respectively oriented at a first tilt angle (α₁) and a secondtilt angle (α₂) with respect to the X direction, wherein themagnetization state [S1; S2]₁, [S1; S2]₂, [S1; S2]₃, and [S1; S2]₄respectively corresponds to a state A=[+1,+1], a state B=[−1,−1], astate C=[+1,−1], and a state D=[−1,+1], wherein the magnetic state S1 isrespectively +1 or −1 if a magnetization of the first layer is orientedat or opposite the angle α₁, wherein the magnetic state S2 isrespectively +1 or −1 if a magnetization of the second layer is orientedat or opposite the angle α₂, wherein the magnetic states S1 and S2 areindependent of each other, wherein the first magnetic layer and thesecond magnetic layer have a magnetic hard axis respectively oriented ata first tilt angle (α₁*) and a second tilt angle (α₂*) with respect tothe X direction, wherein both α₁* and α₂* differ from 0, 90, 180 and 270degrees, and wherein −90<α₁*<0 and/or −90<α₂*<0; after said readingW(x), identifying from W(x), a set (T) of magnetization statetransitions, wherein either 1) the set (T) consists of T_(ij)(x) if W(x)has a pulse shape that is distinctive and distinguishable from thereadback pulse shape of each other magnetization state transition of allpossible magnetization state transitions so as to uniquely identifyT_(ij)(x) or 2) the set (T) comprises T_(ij)(x) and at least one othermagnetization state transition of the all possible magnetization statetransitions whose associated readback pulse shape is not distinctive anddistinguishable from the readback pulse shape of W(x); if the set Tcomprises T_(ij)(x) and the at least one other magnetization statetransition, then reading, by the magnetic read head moving in the Xdirection, a next M readback pulse shapes denoted as W(x₁), W(x₂), . . .W(x_(M)) corresponding to the next M magnetization state transitionsread by the magnetic read head at positions x₁, x₂, . . . , x_(M)(x<x₁<x₂< . . . <x_(M)) in the magnetic medium along the X direction,wherein M is at least 1, wherein W(x_(M)) has a shape that isdistinctive and distinguishable from the readback pulse shape of allother magnetization state transitions of the all possible magnetizationstate transitions, and wherein W(x) together with the next M readbackpulse shapes uniquely identify T_(ij)(x); identifying the magnetizationstate transition T_(ij)(x) from W(x) if the set (T) consists ofT_(ij)(x) or from W(x) together with the next M readback pulse shapes ifthe set (T) comprises T_(ij)(x) and the at least one other magnetizationstate transition; displaying and/or recording the identifiedmagnetization state transition T_(ij)(x).
 14. The computer system ofclaim 13, wherein the set T consists of T_(ij)(x).
 15. The computersystem of claim 13, wherein the set T comprises T_(ij)(x) and the atleast one other magnetization state transition.
 16. A structurecomprising a multi-layer continuous magnetic medium comprising aplurality of magnetic layers, each magnetic layer comprising magneticmaterial continuously distributed in an X-Y plane defined by an Xdirection and a Y direction orthogonal to each other, consecutivemagnetic layers separated by non-magnetic spacer material anddistributed along a Z direction orthogonal to the X-Y plane, wherein theplurality of magnetic layers comprise a first magnetic layer and asecond magnetic layer, wherein the first magnetic layer and the secondmagnetic layer have a magnetic easy axis respectively oriented at afirst tilt angle (α₁) and a second tilt angle (α₂) with respect to the Xdirection, wherein both α₁ and α₂ differ from 0, 90, 180, and 270degrees, wherein the first magnetic layer and the second magnetic layerhave a magnetic hard axis respectively oriented at a first tilt angle(α₁*) and a second tilt angle (α₂*) with respect to the X direction,wherein (−80 ≦α₁*≦−10 and −180<α₂*<−90) or (−180<α₁*<−90 and−80≦α₂*≦−10) or (−80≦α₁*≦−10 and −90<α₂*<0) or (−90<α₁*<0 and−80≦α₂*≦−10), wherein the structure comprises a magnetization state [S1;S2] consisting of a magnetic state (S1) in the first magnetic layer anda magnetic state (S2) in the second magnetic layer; wherein magneticstates (S1) and (S2) are independent of each other; wherein the magneticstate S1 is respectively +1 or −1 if a magnetization of the firstmagnetic layer is oriented at or opposite to the angle α₁; wherein themagnetic state S2 is respectively +1 or −1 if a magnetization of thesecond magnetic layer is oriented at or opposite to the angle α₂;wherein the magnetization state [S1; S2] is a state A=[+1,+1], a stateB=[−1,−1], a state C=[+1,−1], or a state D=[−1,+1].
 17. The structure ofclaim 16, wherein (−80≦α₁*≦−10 and −180<α₂*<−90) or (−180<α₁*<−90 and−80≦α₂*≦−10).
 18. The structure of claim 16, wherein (−80≦α₁*≦−10 and−90<α₂*<0) or (−90<α₁*<0 and −80≦α₂*≦−10).
 19. The structure of claim16, wherein |α₁|≠|α₂.
 20. The structure of claim 16, wherein themagnetization state [S1; S2] was written by a magnetic field in thefirst magnetic layer and the second magnetic layer has a magnetic fieldstrength of H₁ and H₂ and is oriented at a field angle φ₁ and φ₂ withrespect to the X direction in the first magnetic layer and the secondmagnetic layer, respectively; wherein the first magnetic layer and thesecond magnetic layer have a switching field H_(sw,1)(φ₁) andH_(sw,2)(φ₂), respectively; wherein α₁, α₂, H₁, H₂ , φ₁, and φ₂ satisfya relationship (R) selected from the group consisting of a relationshipR1 a, a relationship R1 b, a relationship R1 c, a relationship R1 d, arelationship R1 e, a relationship R1 f, a relationship R2 a, arelationship R2 b, a relationship R2 c, a relationship R2 d, arelationship R2 e, and a relationship R2 f; wherein if [S1; S2] is A orB, then R is R1 a, R1 b, R1 c, R1 d, R1 e, or R1 f; wherein if [S1; S2]is C or D, then R is R2 a, R2 b, R2 c, R2 d, R2 e, or R2 f; saidrelationship R1 a is −80≦α₁*≦−10, α₁*<φ₁<0, H₁≧H_(sw,1)(φ₁),−180<α₂*<−90, α₂ *<φ₂<0, H₂≧H_(sw,2)(φ₂); said relationship R2 a is−80≦α₁*≦−10, −90<φ₁<α₁*, H₁≧H_(sw,1)(φ₁), −180<α₂*<−90, α₂*<φ₂<0,H₂≧H_(sw,2)(φ₂); said relationship R1 b is −180<α₁*<−90, α₁*<φ₁<0,H₁≧H_(sw,1)(φ₁), −80≦α₂*≦−10, α₂*<φ₂<0, H₂≧H_(sw,2)(φ₂); saidrelationship R2 b is −180<α₁*<−90, α₁*<φ₁<0, H₁≧H_(sw,1)(φ₁),−80≦α₂*≦−10, −90<φ_(2<α) ₂*, H₂≧H_(sw,2)(φ₂); said relationship R1 c is−80≦α₁*≦−10, α₁*<φ₁<0, H₁≧H_(sw,1)(φ₁), −90<α₂*<0, α₂*<φ₂<0,H₂≧H_(sw,2)(φ₂); said relationship R2 c is −80≦α₁*≦−10, −90<φ₁<α₁*,H₁≧H_(sw,1)(φ₁), −90<α₂*<0, α₂*<φ₂<0, H₂≧H_(sw,2)(φ₂); said relationshipR1 d is −90<α₁*<0, α₁*<φ₁<0, H₁≧H_(sw,1)(φ₁), −80≦α₂*≦−10, α₂*<φ₂<0,H₂≧H_(sw,2)(φ₂); said relationship R2 d is −90<α₁*<0, α₁*<φ₁<0,H₁≧H_(sw,1)(φ₁), −80≦α₂*≦−10, −9021 φ₂<α₂*, H₂≧H_(sw,2)(φ₂); saidrelationship R1 e is −80≦α₁*≦−10, −90<φ₁<α₁*, H₁≧H_(sw,1)(φ₁),−90<α₂*<0, −90<φ₂<α₂*, and H₂≧H_(sw,2)(φ₂); said relationship R2 e is−80≦α₁*≦−10, −90<φ₁<α₁*, H₁≧H_(sw,1)(φ₁), −90<α₂*<0, α₂*<φ₂<0,H₂≧H_(sw,2)(φ₂); said relationship R1 f is −90<α₁*<0, −90<φ₁<α₁*,H₁≧H_(sw,1)(φ₁), −80≦α₂*≦−10, −90<φ₂<α₂*, H₂≧H_(sw,2)(φ₂); saidrelationship R2 f is −90<α₁*<0, α₁*<φ₁<0, H₁≧H_(sw,1)(φ₁), −80≦α₂*≦−10,−90<φ₂<α₂*, H₂≧H_(sw,2)(φ₂).